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- Find the curve through the origin in thexy-plane which satisfies y''=2y' and whose tangentat the origin has slope 1.Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. xy² = 18 at point (2,3)Find the slope and the equation of the tangent line to the curve. Use the delta method. Explain briefly and concisely. y = 2x^2 – 2x + 4 at (1, 4)
- Find distance from <0,0,0> to the curveFind the points on the curve y=2x^3 + 3x^2 -12x +3 where the tangent line is horizontal. (x,y) = ( , ) (smaller x-value) (x,y) = ( , ) (larger x-value)Show that the point (2, 4) lies on the curve x3 + y3 - 9xy = 0. Then find the tangent line and normal line to the curve there